Weak amenability of CAT(0)-cubical groups

作者：Guentner Erik; Higson Nigel^*

来源：Geometriae Dedicata, 2010, 148(1): 137-156.

DOI：10.1007/s10711-009-9408-8

• Weak amenability
• CAT(0) cube complexes
• Uniformly bounded representations

We prove that if G is a discrete group that admits a metrically proper action on a finite-dimensional CAT(0) cube complex X, then G is weakly amenable. We do this by constructing uniformly bounded Hilbert space representations pi (z) for which the quantities z (a"") ((g)) are matrix coefficients. Here a"" is a length function on G obtained from the combinatorial distance function on the complex X.

• 出版日期2010-10